An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas

Olga Tveretina; Carsten Sinz; Hans Zantema

doi:10.4204/eptcs.4.2

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arXiv · 0909.5038

An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas

Olga Tveretina·Carsten Sinz·Hans Zantema

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Abstract

Haken proved that every resolution refutation of the pigeonhole formula has at least exponential size. Groote and Zantema proved that a particular OBDD computation of the pigeonhole formula has an exponential size. Here we show that any arbitrary OBDD refutation of the pigeonhole formula has an exponential size, too: we prove that the size of one of the intermediate OBDDs is at least $Ω(1.025^n)$.

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Olga Tveretina, Carsten Sinz, Hans Zantema. 2009-09-28. An Exponential Lower Bound on OBDD Refutations for Pigeonhole Formulas. https://doi.org/10.4204/eptcs.4.2

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